{"id":112091,"date":"2023-08-24T11:00:00","date_gmt":"2023-08-24T05:30:00","guid":{"rendered":"https:\/\/www.mygreatlearning.com\/blog\/?page_id=112091"},"modified":"2025-09-16T18:14:17","modified_gmt":"2025-09-16T12:44:17","slug":"how-to-convert-binary-to-decimal","status":"publish","type":"page","link":"https:\/\/www.mygreatlearning.com\/blog\/how-to-convert-binary-to-decimal\/","title":{"rendered":"Convert Binary To Decimal"},"content":{"rendered":"\n<p>Use this simple tool to quickly convert any binary number into its decimal equivalent. Enter a binary number (composed of 0s and 1s), and click \u2018Convert\u2019 to see the decimal value instantly. This tool is perfect for students, programmers, and anyone working with binary data.<\/p>\n\n\n\n\n<style>\n  :root {\n    --primary-color: #0073e6;\n    --primary-hover: #005bb5;\n    --background-color: #f8f9fa;\n    --card-background: #ffffff;\n    --text-color: #333;\n    --border-color: #e0e0e0;\n    --shadow-color: rgba(0, 0, 0, 0.1);\n    --shadow-hover-color: rgba(0, 0, 0, 0.2);\n  }\n  \n  body {\n      margin: 0;\n      font-family: 'Roboto', sans-serif;\n  }\n\n  .content-wrapper {\n    font-family: 'Roboto', sans-serif;\n    line-height: 1.6;\n    color: var(--text-color);\n    background-color: var(--background-color);\n    padding: 20px;\n    max-width: 800px;\n    margin: 20px auto;\n  }\n\n  h2, h3, h4 {\n    padding-bottom: 5px;\n    margin-top: 30px;\n  }\n\n  p {\n    margin-bottom: 15px;\n  }\n\n  ul, ol {\n    margin-left: 20px;\n    margin-bottom: 15px;\n  }\n  \n  pre {\n      background-color: #e9ecef;\n      padding: 15px;\n      border-radius: 5px;\n      border-left: 5px solid var(--primary-color);\n      white-space: pre-wrap;\n      word-wrap: break-word;\n      font-family: 'Courier New', Courier, monospace;\n  }\n\n  \/* NEW: Container for the table to enable scrolling *\/\n  .table-container {\n      overflow-x: auto;\n      margin: 25px 0;\n      border-radius: 5px;\n      box-shadow: 0 0 20px rgba(0, 0, 0, 0.15);\n      -webkit-overflow-scrolling: touch; \/* Smooth scrolling on iOS *\/\n  }\n  \n  .conversion-table {\n      width: 100%;\n      border-collapse: collapse;\n      font-size: 1em;\n      min-width: 400px; \/* Ensures the table has a minimum width, triggering scroll on small screens *\/\n  }\n\n  .conversion-table thead tr {\n      background-color: var(--primary-color);\n      color: #ffffff;\n      text-align: left;\n      font-weight: bold;\n  }\n\n  .conversion-table th,\n  .conversion-table td {\n      padding: 12px 15px;\n  }\n\n  .conversion-table tbody tr {\n      border-bottom: 1px solid #dddddd;\n  }\n\n  .conversion-table tbody tr:nth-of-type(even) {\n      background-color: #f3f3f3;\n  }\n\n  .conversion-table tbody tr:last-of-type {\n      border-bottom: 2px solid var(--primary-color);\n  }\n  \n  .faq p {\n      background-color: #e9f5ff;\n      border-left: 4px solid #007bff;\n      padding: 10px 15px;\n      margin: 10px 0;\n      border-radius: 4px;\n  }\n  \n  #binary-decimal-converter {\n    font-family: 'Roboto', sans-serif;\n    background-color: var(--card-background);\n    border: 1px solid var(--border-color);\n    padding: 25px;\n    max-width: 800px;\n    border-radius: 10px;\n    box-shadow: 0 4px 8px var(--shadow-color);\n    margin: 20px auto;\n    transition: box-shadow 0.3s ease;\n    text-align: center;\n  }\n\n  #binary-decimal-converter:hover {\n    box-shadow: 0 6px 16px var(--shadow-hover-color);\n  }\n  \n  #binary-decimal-converter p {\n      margin: 15px 0;\n  }\n\n  #binaryInput {\n    width: calc(100% - 24px);\n    padding: 12px;\n    margin: 10px 0;\n    font-size: 16px;\n    border-radius: 5px;\n    border: 1px solid #ccc;\n    box-sizing: border-box;\n  }\n\n  button {\n    width: 100%;\n    padding: 12px;\n    font-size: 16px;\n    background-color: var(--primary-color);\n    color: white;\n    border: none;\n    border-radius: 5px;\n    cursor: pointer;\n    transition: background-color 0.3s, transform 0.2s;\n    font-weight: 500;\n  }\n\n  button:hover {\n    background-color: var(--primary-hover);\n    transform: translateY(-2px);\n  }\n\n  #result {\n    font-size: 18px;\n    color: var(--text-color);\n    margin-top: 20px;\n    font-weight: normal; \n    word-wrap: break-word;\n    min-height: 50px; \n    text-align: left; \n    padding: 10px;\n    background-color: #f8f9fa;\n    border-radius: 5px;\n  }\n\n  @media (max-width: 600px) {\n    .content-wrapper, #binary-decimal-converter {\n      padding: 15px;\n      margin: 10px;\n    }\n\n    #binaryInput, button {\n      font-size: 14px;\n      padding: 10px;\n    }\n\n    #result {\n      font-size: 16px;\n    }\n  }\n<\/style>\n\n<div id=\"binary-decimal-converter\">\n  <h2 id=\"binary-to-decimal-converter\">Binary to Decimal Converter<\/h2>\n  <label for=\"binaryInput\" style=\"display: block; text-align: center;\">Enter Binary Number:<\/label>\n  <div style=\"display: flex; justify-content: center; align-items: center; flex-direction: column; gap: 10px;\">\n    <input type=\"text\" id=\"binaryInput\" placeholder=\"e.g., 1010\">\n    <button onclick=\"convertBinaryToDecimal()\">Convert<\/button>\n  <\/div>\n  <div id=\"result\">Your result will be shown here.<\/div>\n<\/div>\n\n<div class=\"content-wrapper\">\n    <h3 id=\"introduction\">Introduction<\/h3>\n    <p>In Mathematics, a number system is a way of representing numbers. There are four types of number systems, which are:<\/p>\n    <ul>\n        <li>Binary Number System (Base \u2013 2)<\/li>\n        <li>Octal Number System (Base \u2013 8)<\/li>\n        <li>Decimal Number System (Base \u2013 10)<\/li>\n        <li>Hexadecimal Number System (Base \u2013 16)<\/li>\n    <\/ul>\n    <p>Number system plays an important role mostly in all computer gadgets and especially in computer architecture. It is used by computer engineers, communication specialists, networking, and other professionals. Before moving on to binary to decimal conversion, let\u2019s understand both the number systems.<\/p>\n\n    <h3 id=\"what-is-a-binary-number-system\">What is a Binary Number System?<\/h3>\n    <p>A Binary Number System is the simplest form of number system that uses only two digits that is 0 (zero) and 1 (one). It is also called as base 2 numeral system. This number is mostly used in computer architecture and electronic devices.<\/p>\n    <p><strong>Examples of Binary Number System:<\/strong> 01, 101, 1110, 10011, 1011101, and so on.<\/p>\n\n    <h3 id=\"what-is-a-decimal-number-system\">What is a Decimal Number System?<\/h3>\n    <p>A Decimal Number System is a representation of numbers from 0 to 9. The decimal number system is the most common number system used by the general public. These number systems are also known as the base 10 numeral system.<\/p>\n    <p><strong>Example of Decimal Number System:<\/strong> 10, 121, 485, 8483, 82940, and so on.<\/p>\n\n    <h3 id=\"what-is-binary-to-decimal-conversion\">What is Binary to Decimal Conversion?<\/h3>\n    <p>Binary to decimal conversion is done to convert binary number system to decimal number system, which means base 2 numeral system are converted into base 10 numeral system. It is important to know binary to decimal conversion because of computer programming applications. So the machine can understand only binary number system in form of 0 and 1 whereas humans can easily understand decimal number system that includes all 10 digits. So, it is important to understand how to convert binary number systems into decimal number systems.<\/p>\n\n    <h3 id=\"binary-to-decimal-conversion-methods\">Binary to Decimal Conversion Methods<\/h3>\n    <p>There are two main methods for converting binary number systems into decimal number systems. These methods are:<\/p>\n    <ul>\n        <li>Positional Notation<\/li>\n        <li>Doubling<\/li>\n    <\/ul>\n\n    <h4 id=\"conversion-using-positional-notation\">Conversion Using Positional Notation<\/h4>\n    <ol>\n        <li>Write the binary number and count the power of 2 from right to left, starting from 0 onwards.<\/li>\n        <li>Now each binary number has the corresponding power of 2 starting from right to left. So the most significant bit will have the highest power of 2.<\/li>\n        <li>Add the product of the second step<\/li>\n        <li>The final answer will be converted into a decimal number that is base 10.<\/li>\n    <\/ol>\n    <p><strong>Example of Positional Notation<\/strong><\/p>\n    <pre>\nBinary Number: (101)\u2082\nCalculation:\n1 \u00d7 2\u00b2 + 0 \u00d7 2\u00b9 + 1 \u00d7 2\u2070\n= 4 + 0 + 1\n= (5)\u2081\u2080\nSo, the decimal number of (101)\u2082 is (5)\u2081\u2080<\/pre>\n    <p>Similarly we can represent fractional binary numbers into decimals:<\/p>\n    <pre>\nBinary Number: (101.101)\u2082\nCalculation:\n(1 \u00d7 2\u00b2 + 0 \u00d7 2\u00b9 + 1 \u00d7 2\u2070) . (1 \u00d7 2\u207b\u00b9 + 0 \u00d7 2\u207b\u00b2 + 1 \u00d7 2\u207b\u00b3)\n= (4 + 0 + 1) . (0.5 + 0 + 0.125)\n= (5.625)\u2081\u2080\nSo, the decimal number of (101.101)\u2082 is (5.625)\u2081\u2080<\/pre>\n\n    <h4 id=\"conversion-using-doubling\">Conversion Using Doubling<\/h4>\n    <p>Conversion using doubling is one of the simplest ways for converting binary numbers into decimal numbers. We need to take the most signification bit or leftmost digit of the number. Then multiply the digit by 2 and add the second leftmost bit and store the result. Similarly, we need to take the result and multiply it by 2 and take the third leftmost bit and update the result. This process will continue till we reach the least significant bit which is the rightmost bit. Since we are multiplying by 2 so this process is known as Doubling.<\/p>\n    <p><strong>Example of Doubling<\/strong><\/p>\n    <pre>\nBinary Number: (101)\u2082\nStep 1: 1\nStep 2: (1 \u00d7 2) + 0 = 2\nStep 3: (2 \u00d7 2) + 1 = 5\nSo, the decimal number of (101)\u2082 is (5)\u2081\u2080<\/pre>\n\n    <h3 id=\"binary-to-decimal-formula\">Binary to Decimal Formula<\/h3>\n    <p>The formula to convert binary number system into decimal can be represented by,<\/p>\n    <pre>A = xn \u00d7 b\u207f + xn-1 \u00d7 b\u207f\u207b\u00b9 + ... + x\u2081 \u00d7 b\u00b9 + x\u2080 \u00d7 b\u2070<\/pre>\n    <p>Where:<\/p>\n    <ul>\n        <li><b>A<\/b> represents the integer<\/li>\n        <li><b>x<\/b> represents the digit value<\/li>\n        <li><b>b<\/b> represents the base value<\/li>\n    <\/ul>\n    <p><strong>For Example:<\/strong><\/p>\n    <pre>(1000)\u2082 = 1 \u00d7 2\u00b3 + 0 \u00d7 2\u00b2 + 0 \u00d7 2\u00b9 + 0 \u00d7 2\u2070<\/pre>\n\n    <h3 id=\"tabular-representation-of-binary-to-decimal-number\">Tabular Representation of Binary to Decimal Number<\/h3>\n    <!-- NEW: Added div wrapper around the table -->\n    <div class=\"table-container\">\n        <table class=\"conversion-table\">\n            <thead>\n                <tr>\n                    <th>Binary<\/th>\n                    <th>Decimal<\/th>\n                    <th>Binary<\/th>\n                    <th>Decimal<\/th>\n                <\/tr>\n            <\/thead>\n            <tbody>\n                <tr><td>0000<\/td><td>0<\/td><td>1000<\/td><td>8<\/td><\/tr>\n                <tr><td>0001<\/td><td>1<\/td><td>1001<\/td><td>9<\/td><\/tr>\n                <tr><td>0010<\/td><td>2<\/td><td>1010<\/td><td>10<\/td><\/tr>\n                <tr><td>0011<\/td><td>3<\/td><td>1011<\/td><td>11<\/td><\/tr>\n                <tr><td>0100<\/td><td>4<\/td><td>1100<\/td><td>12<\/td><\/tr>\n                <tr><td>0101<\/td><td>5<\/td><td>1101<\/td><td>13<\/td><\/tr>\n                <tr><td>0110<\/td><td>6<\/td><td>1110<\/td><td>14<\/td><\/tr>\n                <tr><td>0111<\/td><td>7<\/td><td>1111<\/td><td>15<\/td><\/tr>\n            <\/tbody>\n        <\/table>\n    <\/div>\n\n    <h3 id=\"how-to-convert-binary-to-decimal\">How to Convert Binary to Decimal<\/h3>\n    <h4 id=\"using-positional-notation\">Using Positional Notation<\/h4>\n    <p><strong>Examples:<\/strong><\/p>\n    <pre>\n(10001)\u2082\n= 1 \u00d7 2\u2074 + 0 \u00d7 2\u00b3 + 0 \u00d7 2\u00b2 + 0 \u00d7 2\u00b9 + 1 \u00d7 2\u2070\n= 16 + 0 + 0 + 0 + 1\n= (17)\u2081\u2080<\/pre>\n    <pre>\n(1000.101)\u2082\n= (1 \u00d7 2\u00b3 + 0 \u00d7 2\u00b2 + 0 \u00d7 2\u00b9 + 0 \u00d7 2\u2070) . (1 \u00d7 2\u207b\u00b9 + 0 \u00d7 2\u207b\u00b2 + 1 \u00d7 2\u207b\u00b3)\n= (8 + 0 + 0) . (0.5 + 0 + 0.125)\n= (8.625)\u2081\u2080<\/pre>\n\n    <h4 id=\"using-doubling\">Using Doubling<\/h4>\n    <p><strong>Examples:<\/strong><\/p>\n    <pre>\n(10011)\u2082\nStart with first digit: 1\n= 1 \u00d7 2 + 0 = 2\n= 2 \u00d7 2 + 0 = 4\n= 4 \u00d7 2 + 1 = 9\n= 9 \u00d7 2 + 1 = 19\nResult: (19)\u2081\u2080<\/pre>\n    <pre>\n(10000101)\u2082\nStart with first digit: 1\n= 1 \u00d7 2 + 0 = 2\n= 2 \u00d7 2 + 0 = 4\n= 4 \u00d7 2 + 0 = 8\n= 8 \u00d7 2 + 0 = 16\n= 16 \u00d7 2 + 1 = 33\n= 33 \u00d7 2 + 0 = 66\n= 66 \u00d7 2 + 1 = 133\nResult: (133)\u2081\u2080<\/pre>\n    <p>Converting binary to decimal is a straightforward process. Each digit in a binary number represents a power of 2. Starting from the rightmost digit, you assign the value of 2 raised to the power of the position of the digit and then sum up these values to get the decimal equivalent. Here\u2019s the general formula:<\/p>\n    <p><code>Decimal Value = (binary digit) * 2^(position)<\/code><\/p>\n    <p>Let\u2019s look at a couple of examples:<\/p>\n    <p><strong>Binary: 1010<\/strong><br>\n    Decimal Value = (1 \u00d7 2\u00b3) + (0 \u00d7 2\u00b2) + (1 \u00d7 2\u00b9) + (0 \u00d7 2\u2070)<br>\n    = 8 + 0 + 2 + 0<br>\n    = 10. So, binary 1010 is equal to decimal 10.<\/p>\n    <p><strong>Binary: 110110<\/strong><br>\n    Decimal Value = (1 \u00d7 2\u2075) + (1 \u00d7 2\u2074) + (0 \u00d7 2\u00b3) + (1 \u00d7 2\u00b2) + (1 \u00d7 2\u00b9) + (0 \u00d7 2\u2070)<br>\n    = 32 + 16 + 0 + 4 + 2 + 0<br>\n    = 54. Binary 110110 is equal to decimal 54.<\/p>\n    <p><strong>Binary: 1111<\/strong><br>\n    Decimal Value = (1 \u00d7 2\u00b3) + (1 \u00d7 2\u00b2) + (1 \u00d7 2\u00b9) + (1 \u00d7 2\u2070)<br>\n    = 8 + 4 + 2 + 1<br>\n    = 15. Binary 1111 is equal to decimal 15.<\/p>\n    <p>Remember, the rightmost digit is at position 0, the next to the left is at position 1, and so on. You simply substitute the binary digits into the formula and calculate the decimal value.<\/p>\n    \n    <h3 id=\"binary-to-decimal-conversion-faqs\">Binary to decimal Conversion FAQs<\/h3>\n    <div class=\"faq\">\n        <p><strong>Binary 10101 to Decimal:<\/strong><br>\n        Decimal Value = (1 \u00d7 2\u2074) + (0 \u00d7 2\u00b3) + (1 \u00d7 2\u00b2) + (0 \u00d7 2\u00b9) + (1 \u00d7 2\u2070) = 16 + 0 + 4 + 0 + 1 = 21. <br>\n        Binary 10101 is equal to decimal 21.<\/p>\n        \n        <p><strong>Binary 1011 to Decimal:<\/strong><br>\n        Decimal Value = (1 \u00d7 2\u00b3) + (0 \u00d7 2\u00b2) + (1 \u00d7 2\u00b9) + (1 \u00d7 2\u2070) = 8 + 0 + 2 + 1 = 11. <br>\n        Binary 1011 is equal to decimal 11.<\/p>\n        \n        <p><strong>Binary 11001 to Decimal:<\/strong><br>\n        Decimal Value = (1 \u00d7 2\u2074) + (1 \u00d7 2\u00b3) + (0 \u00d7 2\u00b2) + (0 \u00d7 2\u00b9) + (1 \u00d7 2\u2070) = 16 + 8 + 0 + 0 + 1 = 25. <br>\n        Binary 11001 is equal to decimal 25.<\/p>\n\n        <p><strong>Binary 11111 to Decimal:<\/strong><br>\n        Decimal Value = (1 \u00d7 2\u2074) + (1 \u00d7 2\u00b3) + (1 \u00d7 2\u00b2) + (1 \u00d7 2\u00b9) + (1 \u00d7 2\u2070) = 16 + 8 + 4 + 2 + 1 = 31. <br>\n        Binary 11111 is equal to decimal 31.<\/p>\n\n        <p><strong>Binary 1010111 to Decimal:<\/strong><br>\n        Decimal Value = (1 \u00d7 2\u2076) + (0 \u00d7 2\u2075) + (1 \u00d7 2\u2074) + (0 \u00d7 2\u00b3) + (1 \u00d7 2\u00b2) + (1 \u00d7 2\u00b9) + (1 \u00d7 2\u2070) = 64 + 0 + 16 + 0 + 4 + 2 + 1 = 87. <br>\n        Binary 1010111 is equal to decimal 87.<\/p>\n        \n        <p><strong>Binary 111010 to Decimal:<\/strong><br>\n        Decimal Value = (1 \u00d7 2\u2075) + (1 \u00d7 2\u2074) + (1 \u00d7 2\u00b3) + (0 \u00d7 2\u00b2) + (1 \u00d7 2\u00b9) + (0 \u00d7 2\u2070) = 32 + 16 + 8 + 0 + 2 + 0 = 58. <br>\n        Binary 111010 is equal to decimal 58.<\/p>\n    <\/div>\n\n    <h3 id=\"to-conclude\">To Conclude<\/h3>\n    <p>So, we saw how we can easily convert binary numbers into decimal number systems, making it easier to understand and read. Also, it is important to note that a binary number can also be a decimal number. For example, 10 can be a binary number because it contains 0 and 1, but on the other hand, 10 can also be a decimal number because it uses digits from 0-9. To avoid confusion, always focus on the base value of the number\u2014such as (10)\u2082 for binary (base 2) and (10)\u2081\u2080 for decimal (base 10).<\/p>\n<\/div>\n\n<script>\n  function convertBinaryToDecimal() {\n    const binaryInput = document.getElementById(\"binaryInput\").value.trim();\n    const resultElement = document.getElementById(\"result\");\n\n    if (binaryInput === \"\") {\n        resultElement.innerHTML = \"Please enter a binary number.\";\n        resultElement.style.color = \"#dc3545\";\n        return;\n    }\n\n    if (\/^[01]+$\/.test(binaryInput)) {\n        const decimalValue = parseInt(binaryInput, 2);\n        const len = binaryInput.length;\n        const calculationParts = [];\n        \n        for (let i = 0; i < len; i++) {\n            const digit = binaryInput[i];\n            const power = len - 1 - i;\n            calculationParts.push(`(${digit} \u00d7 2<sup>${power}<\/sup>)`);\n        }\n        const calculationString = calculationParts.join(' + ');\n\n        const outputHTML = `\n            <strong>Answer: ${decimalValue}<\/strong>\n            <br><br>\n            <strong>Calculation Steps:<\/strong><br>\n            (${binaryInput})<sub>2<\/sub> = ${calculationString} = (${decimalValue})<sub>10<\/sub>\n        `;\n        \n        resultElement.innerHTML = outputHTML;\n        resultElement.style.color = \"var(--text-color)\";\n    } else {\n        resultElement.innerHTML = \"Invalid binary number. Please use only 0s and 1s.\";\n        resultElement.style.color = \"#dc3545\";\n    }\n  }\n<\/script>\n\n\n\n\n<p><strong>Suggested Reads:<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><a href=\"https:\/\/www.mygreatlearning.com\/blog\/binary-search-algorithm\/\">What is Binary Search?<\/a><\/li>\n\n\n\n<li><a href=\"https:\/\/www.mygreatlearning.com\/blog\/types-of-data\/\">Types of Data<\/a><\/li>\n<\/ul>\n","protected":false},"excerpt":{"rendered":"<p>Use this simple tool to quickly convert any binary number into its decimal equivalent. Enter a binary number (composed of 0s and 1s), and click \u2018Convert\u2019 to see the decimal value instantly. This tool is perfect for students, programmers, and anyone working with binary data. Binary to Decimal Converter Enter Binary Number: Convert Your result [&hellip;]<\/p>\n","protected":false},"author":41,"featured_media":112099,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"_acf_changed":false,"_uag_custom_page_level_css":"","site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"default","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","ast-disable-related-posts":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"set","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"var(--ast-global-color-4)","background-image":"","background-repeat":"repeat","background-position":"center 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